Slope would be -7/5. The y intercept would be 5.
Answer:
1/3
Step-by-step explanation:
Number cube has 6 sides so a number greater than 4 is 5 and 6. Which is 2 times so 2/6 which can simplify to 1/3
The equation of the quadratic function in standard form as required in the task content is; f(x) = -x² + 12x - 43.
<h3>Standard form equation of a quadratic function.</h3>
It follows from the task content that the standard form equation of the quadratic function is to.be determined.
Since the standard form equation can be derived from the vertex form equation as follows;
f(x) = a (x - h)² + k
f(x) = a (x - 6)² - 7
Hence, to find the value of a, Substitute x = 8 and f(x) = -11 so that we have;
-11 = a (8 - 6)² - 7
-11 = 4a - 7
4a = -4
a = -1.
Hence, the equation in vertex form is; f(x) = -1 (x -6)² - 7 and when expressed in standard form we have;
f(x) = -1(x² - 12x + 36) - 7
f(x) = -x² + 12x - 43
Therefore, the required equation in standard form is; f(x) = -x² + 12x - 43.
Read more on quadratic functions;
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A) x/y = 2/3
B) x + y = 105
Solving Equation A for y
A) y = 1.5x
Substituting A into B
B) x + 1.5x = 105
2.5x = 105
x = 42
y = 63
Answer:
![\sqrt{2} (3\sqrt{2} +\sqrt{14})=6+2\sqrt{7}](https://tex.z-dn.net/?f=%5Csqrt%7B2%7D%20%283%5Csqrt%7B2%7D%20%2B%5Csqrt%7B14%7D%29%3D6%2B2%5Csqrt%7B7%7D)
Step-by-step explanation:
Given : ![\sqrt{2} (3\sqrt{2} +\sqrt{14})](https://tex.z-dn.net/?f=%5Csqrt%7B2%7D%20%283%5Csqrt%7B2%7D%20%2B%5Csqrt%7B14%7D%29)
Solution:
![\sqrt{2} (3\sqrt{2} +\sqrt{14})](https://tex.z-dn.net/?f=%5Csqrt%7B2%7D%20%283%5Csqrt%7B2%7D%20%2B%5Csqrt%7B14%7D%29)
![3*2+\sqrt{28})](https://tex.z-dn.net/?f=3%2A2%2B%5Csqrt%7B28%7D%29)
![6+2\sqrt{7}](https://tex.z-dn.net/?f=6%2B2%5Csqrt%7B7%7D)
Thus , ![\sqrt{2} (3\sqrt{2} +\sqrt{14})=6+2\sqrt{7}](https://tex.z-dn.net/?f=%5Csqrt%7B2%7D%20%283%5Csqrt%7B2%7D%20%2B%5Csqrt%7B14%7D%29%3D6%2B2%5Csqrt%7B7%7D)
Thus the solution is irrational since square root 7 does not have a perfect square and equal to 6+2square root of 14